Boolean-valued second-order logic

Daisuke Ikegami, Jouko Väänänen

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more robust than full second-order logic. Its validity is absolute under forcing, and its Hanf and Löwenheim numbers are smaller than those of full second-order logic.

Original languageEnglish
Pages (from-to)167-190
Number of pages24
JournalNotre Dame Journal of Formal Logic
Issue number1
Publication statusPublished - 2015
Externally publishedYes


  • Boolean validity
  • Boolean-valued second-order logic
  • Full second-order logic
  • Ω-logic

ASJC Scopus subject areas

  • Logic


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